Nicene and Post-Nicene Fathers, Vol. V:A Treatise on the Spirit and the Letter.: Chapter 35

The one was therefore old, because the other is new. But whence comes it that one is old and the other new, when the same law, which said in the Old Testament, “Thou shalt not p. 98covet,” 860
is fulfilled by the New Testament? “Because,” says the prophet, “they continued not in my covenant, I have also rejected them, saith the Lord.” 861
It is then on account of the offence of the old man, which was by no means healed by the letter which commanded and threatened, that it is called the old covenant; whereas the other is called the new covenant, because of the newness of the spirit, which heals the new man of the fault of the old. Then consider what follows, and see in how clear a light the fact is placed, that men who bare faith are unwilling to trust in themselves: “Because,” says he, “this is the covenant which I will make with the house of Israel; After those days, saith the Lord, I will put my law in their inward parts, and write it in their hearts.” 862
See how similarly the apostle states it in the passage we have already quoted: “Not in tables of stone, but in fleshy tables of the heart,” 863
because “not with ink, but with the Spirit of the living God.” 864
And I apprehend that the apostle in this passage had no other reason for mentioning “the New Testament” (“who hath made us able ministers of the New Testament; not of the letter, but of the spirit”), than because he had an eye to the words of the prophet, when he said “Not in tables of stone, but in fleshy tables of the heart,” inasmuch as in the prophet it runs: “I will write it in their hearts.” 865